Blind channel estimation for MIMO OFDM communication systems

BLIND CHANNEL ESTIMATION FOR MIMO
OFDM COMMUNICATION SYSTEMS
CHEN XI
NATIONAL UNIVERSITY OF SINGAPORE
2009
BLIND CHANNEL ESTIMATION FOR MIMO
OFDM COMMUNICATION SYSTEMS
CHEN XI
(M.Sc., National University of Singapore, Singapore)
A THESIS SUBMITTED
FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
DEPARTMENT OF ELECTRICAL AND COMPUTER
ENGINEERING
NATIONAL UNIVERSITY OF SINGAPORE
Acknowledgments
I would like to express grateful appreciation and gratitude to my supervisor, Dr. A.
Rahim Leyman, and co-supervisor, Dr. Liang Ying Chang, for their supports and
guidance during the course of my studies. Their advice and guidance on ways of
performing research are most invaluable and on many occasions, have served as a
driving force for me to keep on going. I have learned enormously from them not
only how to do research, but also how to communicate effectively. Especially, I am
indebted to Dr. Leyman for his great concern in matters outside of academics during
these years, and his readiness to assist me in my future road-map.
I would also like to thank all friends at Institute for Infocomm Research (I2R)
and National University of Singapore (NUS) who have supported me and given me
much joy during these years.
In addition, I am grateful to I2R for providing me with conductive environment
and facilities needed to complete my course of studies.
The completion of this thesis would not be possible without the love and support
of my mother. She has been there for me whenever I needed a helping hand. I also
thank my father who passed away in August 1998. He is always my moral support

and is always together with me in my heart.
3
Contents
Acknowledgements 3
Summary 8
1 Introduction 1
1.1 Towards Fourth Generation Mobile Systems . . . . . . . . . . . . . . . . . . 1
1.2 OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.1 Wideband Air-interface Design Using OFDM . . . . . . . . . . . . . 6
1.2.2 Main Advantages and Disadvantages of OFDM . . . . . . . . . . . . 9
1.2.3 MIMO-OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Blind Channel Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Blind Source Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.5 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2 MIMO-OFDM System Model 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 The Multipath Fading Channel . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Orthogonal Frequency Division Multiplexing . . . . . . . . . . . . . . . . . 23
2.3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.2 Principles of OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4
Contents 5
2.3.3 FFT Based OFDM and System Model . . . . . . . . . . . . . . . . . 27
2.3.4 Zero Padded-OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.4 MIMO-OFDM System Model . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.1 Basic Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.4.2 MIMO-OFDM System Model . . . . . . . . . . . . . . . . . . . . . . 39
2.4.3 Zero Padded MIMO-OFDM . . . . . . . . . . . . . . . . . . . . . . . 46
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3 Subspace-Based Blind Channel Estimation for MIMO-OFDM Systems 48

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 System Model and Basic Assumptions . . . . . . . . . . . . . . . . . . . . . 51
3.3 Subspace-Based Blind Channel Estimator . . . . . . . . . . . . . . . . . . . 52
3.3.1 Second Order Statistics of the MIMO-OFDM Symbols . . . . . . . . 52
3.3.2 Proposed Channel Estimation Algorithm . . . . . . . . . . . . . . . 54
3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4.1 Identifiability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.4.2 Comparison with the Existing Algorithm . . . . . . . . . . . . . . . 60
3.4.3 Asymptotic Performance Analysis . . . . . . . . . . . . . . . . . . . 62
3.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4 Blind Channel Estimation For Linearly Precoded MIMO-OFDM Sys-
tems 74
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.3 Proposed Blind Channel Estimation . . . . . . . . . . . . . . . . . . . . . . 78
Contents 6
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4.1 Identifiability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4.2 Precoder Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4.3 SNR Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4.4 Asymptotic Performance Analysis . . . . . . . . . . . . . . . . . . . 86
4.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
5 A Geometric Method for BSS of Digital Signals with Finite Alphabets 96
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
5.3 Proposed Source Separation Algorithm . . . . . . . . . . . . . . . . . . . . . 100
5.3.1 Real Case: M-ASK Alphabets . . . . . . . . . . . . . . . . . . . . . . 100
5.3.2 Extension to The Complex Case: QAM Alphabets . . . . . . . . . . 103

5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6 Blind MIMO-OFDM Channel Estimation Based on Spectra Correla-
tions 109
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.3 Proposed Blind Estimation Algorithm . . . . . . . . . . . . . . . . . . . . . 115
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4.1 Identifiability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.4.2 Two Practical Examples . . . . . . . . . . . . . . . . . . . . . . . . . 121
Contents 7
6.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7 Conclusion 131
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
7.2 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Appendix 135
A The Proof of Theorem 3.4.3 135
A.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
A.2 Proof of Theorem 3.4.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
B The Proof of Theorem 4.4.2 145
C The Proof of Theorem 4.4.3 153
Summary
The main contribution of this thesis is the development of three blind channel esti-
mation and one blind source separation algorithms for MIMO-OFDM systems. The
first proposed channel estimation algorithm is a subspace based method. We study
the inherent structure of autocorrelation matrices of the system output and construct
a new criterion function, minimizing which leads to a close form solution of the chan-
nel matrices. The second algorithms is based on the assistance of a non-redundant

linear precoder, which brings in cross-correlations between the signals transmitted
on different subcarriers. For the third one, we exploit the spectra correlation of the
system output. It is shown that when the source signals have distinct spectra corre-
lation, then the channel matrix can be estimated up to a complex scalar and column
permutation. Therefore, the problem of the ambiguity matrix in many of the exist-
ing blind channel estimation algorithm can be avoided. The blind source separation
algorithm proposed in this thesis is a geometric based non-iterative algorithm based
on the assumption that the source signal has finite alphabet. The proposed algo-
rithm compares favorably with the existing hyperplane-based and kurtosis-based
algorithms.
8
List of Figures
1.1 Current and Future Wireless Communication Systems . . . . . . . . . . . . 2
1.2 Spectrum overlap in OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Diagram of Multipath Fading . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Discrete Time TDL Channel Model . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 OFDM Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 Cyclic extension and pulse shaping of the OFDM symbol . . . . . . . . . . 27
2.5 OFDM Power Spectrum with Different Window Length . . . . . . . . . . . 27
2.6 OFDM System Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.7 A Simplified Schematic Representation of a MIMO-OFDM Transmitter . . 38
2.8 A Simplified Schematic Representation of a MIMO-OFDM Receiver . . . . 38
2.9 Block Diagram of a MIMO-OFDM . . . . . . . . . . . . . . . . . . . . . . . 40
3.1 NRMSE performance as a function of SNR . . . . . . . . . . . . . . . . . . 67
3.2 BER performance as a function of SNR . . . . . . . . . . . . . . . . . . . . 67
3.3 NRMSE performance as a function of SNR . . . . . . . . . . . . . . . . . . 69
3.4 BER performance as a function of SNR . . . . . . . . . . . . . . . . . . . . 69
3.5 NRMSE performance as a function of SNR . . . . . . . . . . . . . . . . . . 71
3.6 BER performance as a function of SNR . . . . . . . . . . . . . . . . . . . . 71
9

List of Figures 10
4.1 Linearly Precoded MIMO-OFDM System Block Diagram . . . . . . . . . . 76
4.2 NRMSE as a function of parameter φ . . . . . . . . . . . . . . . . . . . . . 89
4.3 NRMSE performance as a function of SNR . . . . . . . . . . . . . . . . . . 91
4.4 BER performance as a function of SNR . . . . . . . . . . . . . . . . . . . . 91
4.5 NRMSE performance as a function of NOS . . . . . . . . . . . . . . . . . . 92
4.6 BER performance as a function of NOS . . . . . . . . . . . . . . . . . . . . 92
4.7 NRMSE performance of “reference” and “normal” channels as functions of
SNR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.1 Symbol Error Rate (SER) Versus SNR . . . . . . . . . . . . . . . . . . . . 108
6.1 NRMSE performance as a function of SNR . . . . . . . . . . . . . . . . . . 127
6.2 BER performance as a function of SNR . . . . . . . . . . . . . . . . . . . . 127
6.3 NRMSE performance as a function of SNR . . . . . . . . . . . . . . . . . . 129
6.4 BER performance as a function of SNR . . . . . . . . . . . . . . . . . . . . 129
List of Symbols
M
t
: Number of transmit antennae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
M
r
: Number of receive antennae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
N
c
: Number of subcarriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
N
g
: Length of Guard Interval (GI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
N: Length of OFDM symbol with GI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
s
i

(k, n): Source rignal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
s(k, n): k
th
block of MIMO-OFDM symbol through n
th
subchannel . . . . . . . . . . . . . 40
s(k): k
th
MIMO-OFDM symbol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
¯
u(k): k
th
modulated MIMO-OFDM symbol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
u(k): k
th
modulated MIMO-OFDM symbol with GI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
F
N
c
: FFT matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
F
cp
: FFT and GI adding matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .41
⊗: Kronecker product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
I
x
: x × x identity matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
h(l): l
th
tap coefficients matrix of the FIR channel . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

x
i
(k, n): Received signal before removing GI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42
x(k, n): k
th
block of received MIMO-OFDM symbol through n
th
subchannel before
11
List of Figures 12
removing GI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
x(k): k
th
received MIMO-OFDM symbol before removing GI . . . . . . . . . . . . . . . . . . . 42
˙
T
N
(h): N × N lower triangular Toeplitz matrices constructed by h . . . . . . . . . . . . . 43
¨
T
N
(h): N × N upper triangular Toeplitz matrices constructed by h . . . . . . . . . . . . 43
y
i
(k, n): Received signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
y(k, n): k
th
block of received MIMO-OFDM symbol through n
th
subchannel . . . . 44

y(k): k
th
received MIMO-OFDM symbol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
R
s
(κ): Autocorrelation matrix of the source signal with block lag κ . . . . . . . . . . . . 52
R
x
(κ): Autocorrelation matrix of the received signal before removing the CP . . . 52
σ
2
v
: Noise power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
R
x
(κ): Constructed by R
x
(κ) 

κ
j=−κ
R
x
(j) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
R
s
(κ): Constructed by R
s
(κ) 


κ
j=−κ
R
s
(j) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
C
N
(h): Block circulant matrix constructed from channel matrix h . . . . . . . . . . . . . . 53
NRMSE: Normalized-root-mean-square-error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
.
F
: Frobenius norm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
P: Precoding matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
H
ji
: Frequency domain channel vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
D(H
ji
): diagonal matrix with the elements of H
ji
along its diagonal . . . . . . . . . . . . 77
U
s
: Matrix spanning signal subspace of the autocorrelation matrix . . . . . . . . . . . . . 79
U
n
: Matrix spanning noise subspace of the autocorrelation matrix. . . . . . . . . . . . . .79
Λ
s
: Diagonal matrix with diagonal elements being the singular values . . . . . . . . . . 79

Q
j
: Ambiguity matrix for the channel matrix associated with the j
th
receive an-
tenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
List of Figures 13
(·)
†
: Pseudo-inverse of a matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
E{·}: Statistical expectation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
S: Source sinal matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
H: MIMO channel matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
X: Received signal matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98
W: Whitening matrix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98
R
s
i
(n, τ): Spectra correlation matrix of source signal with lag τ . . . . . . . . . . . . . . . 115
N

: Period of the cyclic spectra correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
N

: Least common multiple of N
c
and N

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Chapter 1

Introduction
1.1 Towards Fourth Generation Mobile Systems
Comparing with the traditional wired communication technologies, wireless commu-
nication is an emerging field, which has seen enormous growth in the last several
years. Market demands for higher cellular density in urban areas, broadband inter-
net wireless, and better data security, while using a minimum amount of frequency
spectrum is driving wireless developments forward at an amazing speed. Ubiquitous
connectivity (i.e., connectivity anytime and anywhere) to the internet, to company’s
intranets, or to other data services is creating room for applications that might not
even be thought of today.
The mobile communication systems are often categorized as different generations
depending on the services offered. Figure 1.1 shows the evolution routine of the
mobile communication systems. The first generation (1G) comprises the analog
frequency-division multiplexing access (FDMA) systems such as the NMT (Nordic
Mobile Telephone) [1] and AMPS (Advanced Mobile Phone Services) [2]. The second
1
Chapter 1. Introduction 2
1G
(Analog)
2G
(Digital)
3G
(IMT-2000)
3G+
2.4 GHz
WLAN
5 GHz
WLAN
High Speed
WLAN

4 G
<50 Mbps <100 Mbps384 kbps144 kbps~ 1.44 kbps
Low
Speed
Medium
Speed
High
Speed
1995 2000 2005 2010+
AMPS
NMT
GSM
D-AMPS
PDC
IS-95
CDMA2000
WCDMA
TD-SCDMA
801.11b
HIPERLAN/1
8
0
2
.
1
1
a
/
g
H

I
P
E
R
L
A
N
/
2
M
M
A
C
Figure 1.1: Current and Future Wireless Communication Systems
generation (2G) consists of the first mobile digital communication systems such as
the time-division multiple access (TDMA) based GSM (Global System for Mobile
Communication) [8], D-AMPS (Digital AMPS) [1], PDC (Pacific Digital Cellular) [2]
and the code-division multiple access (CDMA) based system IS-95 [9]. In 1999,
the International Telecommunication Union (ITU) approved an industry standard
for third generation (3G) of mobile communication systems. This standard, called
International Mobile Telecommunications-2000 (IMT-2000) [2], strives to provide
higher data rates than current second-generation (2G) systems. 2G systems are
mainly targeted at providing voice services, while 3G systems will be able to support
a wide range of applications including internet access, voice communications and
mobile videophones. In addition to this, a large number of new applications will
emerge to utilize the permanent network connectivity, such as wireless appliances,
notebooks with built in mobile phones, remote logging, wireless web cameras, car
Chapter 1. Introduction 3
navigation systems, and so forth [10]- [13].
In Europe auctions of 3G licenses of the radio spectrum began in 1999. In the

United Kingdom, 90 MHz of bandwidth [12] was auctioned off for £22.5 billion [13].
In Germany the result was similar, with 100 MHz of bandwidth raising $46 billion
(US) [11]. This represents a value of around $450 Million (US) per MHz. The
length of these license agreements is 20 years [12] and so to obtain a reasonable rate
of return of 8% on investment, $105 Million (US) per MHz must be raised per year.
It is therefore vitally important that the spectral efficiency of the communication
system is maximised, as this is one of the main limitations to providing a low cost
high data rate service.
In parallel to the development of the 3G systems, there has been an increasingly
interesting in high-speed wireless local area networks (WLANs). The WLAN sys-
tems do not offer the same wide area coverage as the 3G mobile systems do, but
within their limited coverage area they provide much higher data rates.
Since the beginning of the 1990’s, WLANs for the 900 MHz, 2.4 GHz and 5
GHz license-free ISM (Industrial, Scientific and Medical) bands have been avail-
able, based on a range of proprietary techniques [6]. In June 1997 the Institute of
Electrical and Electronics Engineers (IEEE) defined an international interoperabil-
ity standard, called IEEE 802.11 [34]. This standard specifies a number of Medium
Access Control (MAC) protocols and three different Physical Layers (PHYs) which
support data rates of 1 Mbps and optionally 2 Mbps. In July 1998 IEEE extended
the IEEE 802.11 standard to IEEE 802.11b which describes a PHY providing a
basic rate of 11 Mbps and a fall-back rate of 5.5 Mbps. Meanwhile, the European
Chapter 1. Introduction 4
Telecommunication Standards Institute (ETSI) specified the European WLAN stan-
dard, called HIPERLAN/1 [35], which defines data rates ranging from 1 Mbps to
20 Mbps. However, in contrast to the IEEE 802.11b, no commercial products have
been developed that support the HIPERLAN/1 standard.
Motivated by the demand for even higher data rates, a new standard called IEEE
802.11a was ratified in 2000, which is based on the OFDM as the transmission
technique for the newly available spectrum in the 5 GHz band. It defines data
rates between 6 and 54 Mbps [59]. To make sure that these data rates are also

available in the 2.4 GHz band, mid 2003 IEEE standardization group issued a similar
standard for this band named IEEE 802.11g [34]. At the same time, the ETSI
working group named Broadband Radio access Networks (BRAN) in Europe and
Multimedia Mobile Access Communication (MMAC) group in Japan published their
new generation of WLAN standards, called HIPERLAN/2 [5] and the MMAC [6]
respectively. Following the selection of OFDM by the IEEE 802.11a standardization
group, both the ETSI BRAN and MMAC working group adopted OFDM for their
PHY.
While the roll-out of 3G systems is under progress, research activities on the
fourth generation (4G) have already started [14]- [17]. According to the increasing
demand of wireless data traffic, it is obvious that the main goal in developing next
generations of wireless communication systems are increasing the link throughput
(i.e., bit rate) and the network capacity. Few of the aims of 4G networks have yet
been published, however it is likely that they will be to extend the capabilities of 3G
networks, allowing a greater range of applications, and improved universal access.
Chapter 1. Introduction 5
Ultimately 4G networks should encompass broadband wireless services, such as High
Definition Television (HDTV) (4-20 Mbps) and computer network applications (1-
100 Mbps). This will allow 4G networks to replace many of the functions of WLAN
systems. In fact, a popular vision suggests to combine WLAN systems for high peak
data rates with cellular systems for wide area-coverage, and to allow inter-system
handovers [18]. On the other hand, cost of service must be reduced significantly
from 3G networks. The spectral efficiency of 3G networks is too low to support
high data rate services at low cost. As a consequence one of the main focuses of 4G
systems will be to significantly improve the spectral efficiency [17].
In addition to high data rates, future systems must support a higher Quality Of
Service (QoS) than current cellular systems, which are designed to achieve 90-95%
coverage [19], i.e. network connection can be obtained over 90-95% of the area of the
cell. This will become inadequate as more systems become dependent on wireless
networking. As a result 4G systems are likely to require a QoS closer to 98-99.5%. In

order to achieve this level of QoS it will require the communication system to be more
flexible and adaptive. In many applications it is more important to maintain network
connectivity than the actual data rate achieved. If the transmission path is very
poor, e.g. in a building basement, then the data rate has to drop to maintain the link.
Thus the data rate might vary from as low as 1 kbps in extreme conditions, to as high
as 20 Mbps for a good transmission path. Alternatively, for applications requiring a
fixed data rate, the QoS can be improved by allocating additional resources to users
with a poor transmission path.
Chapter 1. Introduction 6
1.2 OFDM
1.2.1 Wideband Air-interface Design Using OFDM
Multipath propagation is the primary issue in the air-interface design for wideband
(high data-rate) communication systems. Multiple replicas of the transmitted sig-
nal arrive at the receiver with various propagation delays, due to reflections on all
kinds of objects and obstacles in the environment. Therefore, if a high-rate data
stream is transmitted on such a channel, multiple data symbols interfere with each
other, making the data recovery difficult. This phenomenon is called “inter-symbol-
interference” (ISI). The standard solution to the ISI problem is to design a linear
filter at the receiver side that employs a means for compensating or reducing the ISI
in the received signal. This compensation method is called equalization. The main
challenge is to adapt the filter coefficients to the time-variant channel conditions.
The adaptation could be computationally extremely demanding, particularly if long
filters are required as in the case where the channel impulse response spans many
data symbols.
Fortunately, Orthogonal Frequency Division Multiplexing (OFDM) can drasti-
cally simplify the equalization problem [6]. In OFDM, the high-rate serial data
stream is split up into a number (several dozens up to a few thousand) of paral-
lel data streams at a much lower (common) symbol rate, which are modulated on
a set of subcarriers (frequency division multiplexing). High spectral efficiency is
achieved by selecting a specific (orthogonal) set of subcarrier frequencies. Inter-

carrier-interference is avoided due to the orthogonality, although the spectra of the
subcarriers actually overlap (see Figure 1.2) [6]. The idea is to make the symbol
Chapter 1. Introduction 7
Frequency
Magnitude
Subcarrrier
Frequency
Spacing
Figure 1.2: Spectrum overlap in OFDM
period long with respect to the channel impulse response in order to reduce ISI.
This implies that the bandwidth of the subcarriers gets small (with respect to the
channel’s coherence bandwidth [25]), thus the impact of the channel is reduced to
an attenuation and phase distortion of the subcarrier symbols (“flat fading”), which
can be compensated by efficient one-tap equalization.
Thus, it is quite attractive in the robustness against frequency selective fading,
especially for high-speed data transmission [26]. In practice, OFDM has already
been used in European digital audio broadcasting (DAB), digital video broadcasting
(DVB) systems and high performance radio local area network (HIPERLAN) [23]-
[24], [27]. Furthermore, combined with Multiple-Input Multiple-Output (MIMO)
wireless technology, OFDM has been recognized as one of the most promising tech-
niques for the future 4G systems [10].
The first study of OFDM was published by Chang in 1966 [24]. He presents
Chapter 1. Introduction 8
a principle for transmitting messages simultaneously through a linear bandlimited
channel without interchannel (ICI) and intersymbol interference (ISI). In 1971, a
major contribution to OFDM was presented by Weinstain and Ebert [25], who
used the discrete Fourier transform (DFT) to perform baseband modulation and
demodulation. This technique involved assembling the input information into blocks
of N
c

complex symbols, one for each subchannel. An inverse FFT is performed on
each block, and the resultant transmitted serially. At the receiver, the information is
recovered by performing an FFT on the received block of signal samples. This form
of OFDM is often referred to as Discrete Multi-Tone (DMT). The most significant
advantage of this DMT approach is the the efficiency of the FFT algorithm. An
N
c
-point FFT requires only on the order of N
c
log N
c
multiplications, rather than
N
2
c
as in a straightforward computation.
Another important contribution was due to Peled and Ruiz in 1980 [26], who
introduced the cyclic prefix (CP) or cyclic extension, solving the orthogonality prob-
lem. Instead of using an empty guard space, they filled the guard space with a cyclic
extension of the OFDM symbol. This effectively simulates a channel performing
cyclic convolution, which implies orthogonality over dispersive channels when the
CP is longer than the impulse response of the channel [24], [26]. This introduces an
energy loss proportional to the length of CP, but the zero ISI generally motivates
the loss.
Chapter 1. Introduction 9
1.2.2 Main Advantages and Disadvantages of OFDM
The advantages of OFDM, especially in the multipath propagation, interference
and fading environment, make the technology a promising alternative in digital
communications including mobile multimedia. The advantages of OFDM are:
• Efficient use of the available bandwidth since the subchannels are overlapping.

• Spreading out the frequency fading over many symbols. This effectively ran-
domizes the burst errors caused by the Rayleigh fading, so that instead of
several adjacent symbols (in time on a single-carrier) being completely de-
stroyed, (many) symbols in parallel are only slightly distorted.
• The symbol period is increased and thus the sensitivity of the system to delay
spread is reduced.
On the other hand, there are also problems associated with OFDM system design:
• OFDM signal is contaminated by non-linear distortion of transmitter power
amplifier, because it is a combined amplitude-frequency modulation (it is nec-
essary to maintain linearity).
• OFDM is very sensitive to carrier frequency offset caused by the jitter of carrier
wave and Doppler effect caused by moving of the mobile terminal.
1.2.3 MIMO-OFDM
Research in the information theory, performed in the early 90’s, has revealed that
important improvement in spectral efficiency can be achieved when multiple anten-
nae are applied at both the transmitter and receiver side, especially in rich-scattering
Chapter 1. Introduction 10
environments. This has been shown for wireless communication links in both nar-
rowband channels [28] as well as wideband channels [29], and it initiated a lot
of research activity to practical communication schemes that exploit this spectral-
efficiency enhancement. The resulting multiple-transmit multiple-receive antenna,
i.e., Multiple-Input Multiple-Output (MIMO), techniques can basically be split into
two groups: Space-Time Coding (STC) [30]- [32] and Space Division Multiplexing
(SDM) [28], [29], [33]. STC increases the robustness / performance of the wire-
less communication system by transmitting different representations of the same
data stream (by means of coding) on the different transmitter branches, while SDM
achieves a higher throughput by transmitting independent data streams on the dif-
ferent transmitter branches simultaneously and at the same carrier frequency.
The highest spectral efficiency gains are achieved when the individual channels
from every transmit antenna to every receive antenna can be regarded to be inde-

pendent. In practice this is the case in rich-scattering environments with no Line
of Sight (LOS) path present between transmitter and receiver. So, especially for
enhancement of the throughput of wireless applications in rich-scattering environ-
ment, MIMO techniques are appealing. In general, MIMO can be considered as an
extension to any Single-Input Single-Output (SISO), Single-Input Multiple-Output
(SIMO), i.e., receiver diversity, or Multiple-Input Multiple-Output (MISO), i.e.,
transmit diversity, system operating in these environments.
The WLAN standards IEEE 802.11b, IEEE 802.11a/g indicate that they are
usually deployed in an indoor environment, while the probability of having no direct
communication path between transmitter and receiver is high [34]. So, we can
Chapter 1. Introduction 11
conclude that the deployment conditions of WLAN systems are most favorable for
applying MIMO. In fact, these standards are the WLAN standards that currently
gain the most momentum. They are both based on OFDM. Thus the robustness
of OFDM against frequency-selective fading and the favorable properties of indoor
radio channels for MIMO techniques lead to the very promising combination of
MIMO-OFDM as potential solution to satisfy the main goals in developing next
generations of wireless communication systems. As such, MIMO-OFDM techniques
are attractive candidates for high data rate extensions of the IEEE 802.11a and
802.11g standards. As an example the IEEE 802.11 Task Group ’n’ (TGn) can be
mentioned which is planning to define high-data rate WLAN extensions up to 250
Mbps [34].
1.3 Blind Channel Estimation
As mentioned in the previous section, multipath propagation is the primary issue in
the wideband wireless communication systems. In order to recover the transmitted
signal at the receiver, it is essential to know some information about the channel.
The cancellation of channel effects is referred to as equalization. It is possible
to construct the equalizer directly without explicitly estimating the channel, or
indirectly, by first estimating the channel. In either case, the transmitter should
send a signal known a priori by the receiver which is called training. However, most

wireless devices will be battery powered. Hence the transmission of training signals
will seriously affect the longevity of such devices. Moreover, training increases the
overhead of the transmitted signal, thus reducing the net data transmission rate.
Chapter 1. Introduction 12
Thus, it is reasonable to use blind channel estimation methods to possibly reduce
the amount of training required significantly. Typically, some special property of
the transmitted signal is exploited for blind channel estimation.
Blind equalization methods provide attractive solutions since they do not re-
quire any known transmitted data for channel estimation and equalization pur-
poses [4], [39]- [42]. Instead, they use the statistical and structural properties of the
communication signals (Finite alphabet, constant modulus, sub-spaces orthogonal-
ity). Channel identification or equalization requires that information about both the
channel amplitude and phase responses can be acquired from the received signal.
A symbol rate sampled communications signal is typically wide sense stationary
(WSS). Second order statistics from a WSS process contain no phase information.
Hence one can not distinguish between minimum phase and non-minimum phase
channels. Therefore, other statistical properties of the signal have to be used to
extract the phase information.
The communication signals are typically non-Gaussian. Hence, the Higher Order
Statistic (HOS) of the signals are non-zero and may also be exploited in equalization.
HOS retain the phase information as well [36]. Early blind algorithms were either
implicitly or explicitly based on HOS. In time domain, HOS are represented by
higher than second order cumulants and moments. However, Higher order statistics
and spectra may not provide a feasible approach for constructing practical equal-
izers. They have a large variance and consequently large sample sets are needed
in order to obtain reliable channel estimates. This is a severe drawback, in partic-
ular in applications where the channel is time varying, data rates are high or low